Stark Effect

Overview

The Stark Effect, named after German physicist Johannes Stark, is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. The amount of shifting or splitting is proportional to the strength of the electric field. This is an important phenomenon in both atomic physics and quantum mechanics.

Basic Theory and Linear Stark Effect

The Stark Effect arises due to the interaction of an external electric field with the electric dipole moment of an atom or molecule. In the presence of an electric field , the potential energy of an atom or molecule with a dipole moment is given by:

For hydrogen-like atoms, where the potential energy of the atom can be solved exactly, the linear Stark effect can be observed, in which the energy levels split linearly with the electric field. The change in energy due to the Stark effect is given by:

where is the wavefunction of the atom.

Quadratic Stark Effect

In more complex atoms, the linear Stark effect usually disappears because atomic wavefunctions are typically chosen to be real, leading to zero for the expectation value of the dipole moment. However, these atoms display the quadratic Stark effect where the energy levels shift proportional to the square of the electric field strength. The quadratic Stark effect is often observed in atoms with higher atomic number.

The quadratic Stark shift in energy can be approximated using second-order perturbation theory, given by:

where is the electric dipole operator.

Applications

The Stark effect has wide-ranging applications in spectroscopy and is used as a powerful tool in both laboratory and astronomical spectroscopy. It is also applied in the study of electric field effects in semiconductors and superconductors, and in the design of electro-optical devices based on the Stark effect.

Do you prefer video lectures over reading a webpage? Follow us on YouTube to stay updated with the latest video content!

Want to study more? Visit our Index here!